Question: Reduce to lowest terms: $- \dfrac{5}{6} \div \dfrac{9}{4} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{9}{4}$ is $ \dfrac{4}{9}$ Therefore: $ - \dfrac{5}{6} \div \dfrac{9}{4} = - \dfrac{5}{6} \times \dfrac{4}{9} $ $ \phantom{- \dfrac{5}{6} \times \dfrac{4}{9}} = \dfrac{-5 \times 4}{6 \times 9} $ $ \phantom{- \dfrac{5}{6} \times \dfrac{4}{9}} = \dfrac{-20}{54} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{-20}{54} = \dfrac{-20 \div 2}{54 \div 2} = -\dfrac{10}{27} $